Xiaomin Xu, Professor, Peking University

Xiangke Chang, Associate Professor

Stokes phenomenon and isomonodromy deformation equations: Explicit solution to the Riemann-Hilbert problem and integrability of the isomonodromy equation

14:50-15:40 November 28(Monday), Tencent Meeting ID: 685-791-351

Stokes phenomenon states that the asymptotic behavior of functions can differ in different regions of the complex plane, and that these differences can be described in a quantitative way. These quantities, the so-called Stokes matrices, have played important roles in the study of integrable systems, representation theory, quantum field theory, differential and algebraic geometries and so on. 

Motivated by the representation theory of quantum groups, the second talk then solves the Riemann-Hilbert problem of the meromorphic linear system of ordinary differential equations, and derives an asymptotic expansion, as well as a connection formula, of the solutions of the nonlinear isomonodromy equation.